Chern-Weil-Lecomte morphism for L∞-algebras - Carmona, Juan Sebastian Herrera (2022)
In this thesis we extend the Chern-Weil-Lecomte morphism to the setting of extensions of L∞-algebras together with a representation up to homotopy. This morphism takes values in the L∞-algebra cohomology with coefficients in a graded vector space. We prove that this construction is natural and that the L∞-algebra cohomology is invariant by equivariant L∞-quasi-isomorphisms. As an application we obtain a Chern-Weil-Lecomte morphism for principal 2-bundles over a Lie groupoid that admit a 2-connection form.